Sintered magnets are metals
It is easy to think of a permanent magnet as a source of field and nothing else. Electrically, sintered NdFeB is a metal alloy with a resistivity in the region of 1.4–1.6 µΩ·m — poor by the standards of copper, but perfectly capable of carrying substantial induced current. Samarium cobalt is similar. Ferrite is not: it is a ceramic with resistivity many orders of magnitude higher, which is why ferrite rotors do not have this problem.
| Material | Resistivity | Eddy current behaviour |
|---|---|---|
| Sintered NdFeB | ~1.4–1.6 µΩ·m | Conducts readily; segmentation usually required at speed |
| Sintered SmCo | ~0.8–0.9 µΩ·m | Conducts more than NdFeB; tolerates the resulting heat far better |
| Bonded NdFeB | Orders of magnitude higher | Polymer matrix isolates the particles; losses largely absent |
| Ferrite / ceramic | Effectively insulating | Negligible eddy loss |
| Electrical steel | ~0.4–0.6 µΩ·m | Why laminations exist in the first place |
The reason this matters more in the magnet than in the stator is not the material — the steel actually conducts better. It is that the stator was laminated from the start and the magnet was not. A stack of 0.35 mm laminations has already broken the current paths. A solid magnet block 40 mm long presents an uninterrupted conductor.
Rotor magnets sit inside a rotating body, separated from the cooling by an air gap that is an excellent thermal insulator. Loss generated in the magnet has almost nowhere to go, so a modest wattage produces a disproportionate temperature rise — and rising temperature raises the demagnetization knee, which is the one direction a rotor magnet must not travel. This is a self-reinforcing failure: hotter magnet, lower coercivity, more susceptibility, and the loss does not decrease.
Where the harmonics come from
A magnet rotating in perfect synchronism with a perfectly sinusoidal field would see a constant flux and carry no induced current at all. Real machines are not that, and each departure is a harmonic the rotor sees as an alternating field.
Two features of this list drive the design consequence. First, loss scales with the square of frequency, so the high-order harmonics matter far more than their amplitude suggests — a small ripple at the switching frequency can outweigh a much larger low-order component. Second, the worst case is usually high speed under load with flux weakening active, which is also the condition where the rotor is already hottest.
It is normally chosen for drive efficiency, audible noise and current ripple. It is also a term in the rotor heating budget, and moving it can shift magnet loss noticeably in either direction. If rotor temperature is marginal, the drive settings belong in the conversation alongside the magnet grade.
The loss expression, and what it tells you
For a conducting sheet in an alternating field, with the field uniform and the sheet thin compared with the skin depth, the classical result for power dissipated per unit volume is:
p = loss per unit volume, W/m³
f = frequency of the alternating component, Hz
B = peak amplitude of that component, T
w = dimension across the current path, m
σ = electrical conductivity, S/m
Three of those terms are squared, and that is the whole engineering story.
Note that this expression governs the induced-current loss only. It says nothing about hysteresis in the steel, windage, or bearing loss, and it assumes the field is uniform across the piece and that induced currents do not significantly oppose the applied field. That last assumption fails once the piece becomes large compared with the skin depth, at which point the real loss falls below what the formula predicts — so treating it as an upper bound is reasonable, and treating it as precise is not.
skin depth — when w approaches or exceeds δ, the simple expression overstates loss
Segmentation, and why it works so well
Because loss per unit volume goes with the square of the current-path dimension, cutting a magnet into pieces is disproportionately effective. Divide a block into n segments across the current path. Each segment now has a path dimension of w/n, so its loss per unit volume falls by n². The total volume is unchanged, so total loss falls by roughly n² as well.
idealised: n electrically isolated segments across the current path
real gains are smaller — end effects, finite insulation, 3D current paths
| Segments | Ideal loss | Typical realised | Cost impact |
|---|---|---|---|
| 1 (solid) | 100% | 100% | Baseline |
| 2 | 25% | 30–40% | Small — one extra cut and one more part to place |
| 4 | 6% | 12–20% | Moderate; assembly time and tolerance stack grow |
| 8 | 1.6% | 6–12% | Significant; diminishing returns become obvious |
| 16 | 0.4% | 4–10% | Rarely justified — end effects dominate by here |
The gap between ideal and realised widens as segment count rises, which is why the practical answer for most machines lands between two and six. Beyond that, the assembly cost, the added adhesive bond lines and the loss of active magnet volume to insulation gaps outweigh a loss reduction that is already small in absolute terms.
Which way to cut
The other levers
Segmentation is the magnet-side answer, but it is not the only one and often not the cheapest. The loss expression has four terms and three of them live outside the magnet.
| Lever | Acts on | Cost | Notes |
|---|---|---|---|
| Segment the magnets | Path dimension | Assembly time, part count | Most direct; scales as n² |
| Skew rotor or stator | Harmonic amplitude | Tooling, slight torque loss | Also improves cogging and acoustic noise |
| Slot/pole combination | Harmonic content | Design effort only | Cheapest lever if the machine is not yet fixed |
| Magnetic wedges, closed slots | Permeance ripple | Manufacturing complexity | Attacks the largest single source directly |
| Raise switching frequency | Ripple amplitude down, f up | Drive losses | Both terms move — verify, do not assume |
| Non-conductive sleeve | Avoids adding loss | Carbon fibre costs more than steel | A conductive retaining sleeve can dominate total rotor loss |
| Bonded magnets | Conductivity | Substantially lower remanence | Only where the torque budget allows it |
| Higher coercivity grade | Tolerance of the heat | Heavy rare earth content | Treats the symptom; often the pragmatic answer |
The retaining sleeve deserves its own note. High-speed rotors need something holding the magnets against centrifugal load, and a metallic sleeve — Inconel, stainless, titanium — sits in the air gap directly in the harmonic field, in one continuous conducting piece. On some machines it produces more loss than the magnets do. Carbon fibre avoids this entirely and is the standard answer where the budget allows, though it brings its own thermal-expansion and pre-tension design problems.
Every mitigation above reduces heating. None eliminates it. The grade still has to survive the temperature the rotor actually reaches, with margin for the demagnetizing field at peak current. Work the thermal case first and choose the grade against the result — the derating calculator and the permeance coefficient calculator together give the working point at temperature, which is the number that decides whether a grade is adequate.
When eddy currents are the product
Everything above treats induced current as loss. An entire class of devices exists because that loss can be put to work, and the same physics runs in reverse.
Two characteristics follow directly from the physics and shape every one of these applications. The force depends on relative motion, so an eddy-current brake produces nothing at standstill and cannot hold a load. And all the energy removed appears as heat in the conductor, so the conductive disc or drum has to be sized for the thermal duty rather than the mechanical one — which is the usual reason these devices are larger than expected.
For torque through a sealed wall without slip, a synchronous magnetic coupling is the right device, and there the containment shell is a conductive part in a rotating field — the same loss mechanism, this time unwanted, and the reason shells are made thin and increasingly from non-conductive composites.
A metallic containment can in a magnetic coupling sees the full rotating field and dissipates real power as heat into the process fluid. On larger couplings this is kilowatts, and it is a common surprise during commissioning. Where the pressure rating permits, a composite shell removes the loss entirely.